1. Field of the Invention
The present invention relates to methods using distributed approximating functionals (DAF), DAF-wavelets and DAF-neural networks for filtering, denoising, processing, restoring, enhancing, padding, or other signal processing procedures directed to images, signals, 1D, 2D, 3D . . . nD spectra, X-ray spectra, CAT scans, MRI scans, NMR, and other applications that require data processing at or near the theoretical limit of resolutions.
More particularly, the present invention relates to the use of infinitely smooth DAFs in combination with other signal processing techniques to provide methods and apparatuses utilizing such methods that can enhance image, spectral, or other signal data and decrease the time need to acquire images, spectra or other signals.
2. Description of the Related Art
Many techniques currently exist for processing images, refining spectra, analyzing data or the like. Many of these techniques are well-known and used extensively. However, these techniques generally suffer from one or more limitation on their ability to enhance signal or image and construct or restore missing or lost data, especially if the user desires the error inherit in signal acquisition and the error introduced by the processing technique to be as small as possible, i.e., as close as possible to Heisenberg's uncertainty principle.
Thus, there is a need in the art for improved techniques for processing acquired data whether in the form on a image, a spectra, a multidimensional spectra or the like so that the error due to processing can be minimized which can increase resolution and decrease acquisition times.